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Subject: Clever approaches for group-scoring an event? rss

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Chad Ellis
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My father-in-law is participating in a friendly golf tournament with a mix of Americans and Canadians. They want to introduce some group competition so that one country "wins" but since there are about 75% Americans in the tournament the basic bell curve suggests that Americans will tend to have the top and bottom slots. They are looking for a good system to judge the overall performance of a larger group vs. a smaller one.

The mean is an obvious choice...does anyone here know of a better one?
 
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Carl Parsons
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Let Octavian judge.
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Chad_Ellis wrote:
My father-in-law is participating in a friendly golf tournament with a mix of Americans and Canadians. They want to introduce some group competition so that one country "wins" but since there are about 75% Americans in the tournament the basic bell curve suggests that Americans will tend to have the top and bottom slots. They are looking for a good system to judge the overall performance of a larger group vs. a smaller one.

The mean is an obvious choice...does anyone here know of a better one?


How many people are participating?

Median's fine too, although all that does is correct for skewness.

You could look at who has the best trimmed mean -- take the average of the 25th to 75th percentiles. Again, just corrects for skewness.

You could do best score plus worst score and compare too -- that has some fun gamey aspects, but might make the "worst" for each country feel worse.

Honestly, the mean is probably the best bet -- scoring should be straightforward and accessible to participants.
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Scott Russell
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Is there a good way to break the Americans into three teams? Then you could have one of each team per foursome.

Or you could multiply the Canadians' scores by three.

(But mean or median seem way simpler.)
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Paul W
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If nothing else, I agree with median over mean. (or mean of the four middle players from each country, something like that).

Dividing up the US into multiple teams (perhaps by geographic region?) is another option.
 
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Christopher Seguin
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Clearly no one suggested the most obvious and best choice:

Dis-invite the Canadians!

I mean, really, who the hell wants to play golf with Canadians? If it were hockey, ice fishing, or engaging in "adult" activities with moose, then sure, invite the Canadians since they would excel. But golf - really?

(All joking aside, others have suggested "median", and that is probably your best, most fair, approach)
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chrisnd wrote:
Clearly no one suggested the most obvious and best choice:

Dis-invite the Canadians!

I mean, really, who the hell wants to play golf with Canadians? If it were hockey, ice fishing, or engaging in "adult" activities with moose, then sure, invite the Canadians since they would excel. But golf - really?

(All joking aside, others have suggested "median", and that is probably your best, most fair, approach)


Considering most of Canada only has 'golfable' weather for aboot 6 days per year, score comparisons will be irrelevant. laugh

(My GGG Parents immigrated from Canada)
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Christopher Seguin
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rcbevco wrote:
chrisnd wrote:
Clearly no one suggested the most obvious and best choice:

Dis-invite the Canadians!

I mean, really, who the hell wants to play golf with Canadians? If it were hockey, ice fishing, or engaging in "adult" activities with moose, then sure, invite the Canadians since they would excel. But golf - really?

(All joking aside, others have suggested "median", and that is probably your best, most fair, approach)


Considering most of Canada only has 'golfable' weather for aboot 6 days per year, score comparisons will be irrelevant. laugh

(My GGG Parents immigrated from Canada)


I have a friend of mine that lives in Ft. McMurray in Alberta. He will occasionally send me screen shots of his weather ap from his phone, usually during the winter months. I find Cleveland temperatures in January and February to usually be brutal (not this year, Mr. El Nino), but then he reminds me that he lives in the northern reaches of the province, which sometimes gets as high as NEGATIVE 37 DEGREES on a "warm day in February".

6 Days for golfing is "generous" in Canada.
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Robert Stuart
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Match them rank by rank, with the 'average' of the majority in a given rank compared to the score of the minority at that rank. To give an example:

Suppose there are 30 Americans and 11 Canadians. The average score of the top 3 Americans will be compared to the score of the top Canadian. The winning team gets 1 point. The average score of the next 3 Americans will be compared with the score of the second-rank Canadian. The winning team gets 1 point. And so on. The scores of the middle three Canadians will be compared with the average scores of just 2 Americans (since there are only 30 Americans & not 33 in this example). The maximum number of points in this type of matching will be 11 points. The team with the higher score wins.

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bob_santafe wrote:
Match them rank by rank, with the 'average' of the majority in a given rank compared to the score of the minority at that rank. To give an example:

Suppose there are 30 Americans and 11 Canadians. The average score of the top 3 Americans will be compared to the score of the top Canadian. The winning team gets 1 point. The average score of the next 3 Americans will be compared with the score of the second-rank Canadian. The winning team gets 1 point. And so on. The scores of the middle three Canadians will be compared with the average scores of just 2 Americans (since there are only 30 Americans & not 33 in this example). The maximum number of points in this type of matching will be 11 points. The team with the higher score wins.


I'd have to think about it, but I think that's no better than just taking the average in terms of skewing the results towards the team with less participants. (You'd expect more extreme z-scores in the larger group, so you'd expect essentially the same thing the mean would you get if you broke it into quantiles like you're doing.)
 
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Jorge Montero
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They should all score in at least 5 different categories, and then see which team has the highest score in its lowest categories. You can even provide some bonus points that are wild.

But with your father being there, I'd say that the canadians shouldn't play, and instead their score should be the score the average regular player at the course gets, and see if all those American active golfers can really beat the market.
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hibikir wrote:
They should all score in at least 5 different categories, and then see which team has the highest score in its lowest categories. You can even provide some bonus points that are wild.

But with your father being there, I'd say that the canadians shouldn't play, and instead their score should be the score the average regular player at the course gets, and see if all those American active golfers can really beat the market.


Clearly the score should be on the nicest and most polite players. Bonus points for use of 'eh'.

Americans wouldn't stand a chance.

See also...

http://boards.straightdope.com/sdmb/showthread.php?t=441430
Math Problem: Fairest Way to Score with Uneven Teams

There is some interesting discussion and this was proposed by one
Quote:

Here's a thought:

For each team size, compute the average score and standard deviation. For each team, subtract the average score for their team size, and divide by the corresponding standard deviation. Then multiply the new scores by the overall standard deviation, and add the overall mean.

It's kind of a hack, but it makes rough intuitive sense. You're figuring out how different each team's score is from the average for their size in standard units, and then expressing everyone's score in common units.




As long as you specify the rules ahead of time, I'm sure everyone will be happy with the results of trying to balance the smaller and larger teams. Just like the electoral college and presidential elections, for example.

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Vic Lineal
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In a different spirit from previous responses (won't work as scoring and requires data post-treatment), after the fact you can check whether mean scores are significantly different with a t-test. It allows for different team sizes (although it loses resolution as teams are differently sized) but will be rather inconclusive with few people.
 
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Scott Russell
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Randomly select one (or a few) score(s) from each team to compare.
 
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"Accidentally" lose the score cards and give everyone a participation certificate.
 
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TheChin! wrote:
"Accidentally" lose the score cards and give everyone a participation certificate.

No, "accidentally" don't put names on the score cards. Then encourage the idea of taking a card with a better score by whatever means. Last man standing and all that… devil
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